THE NATURAL LAW OF VOLATILITY JUMPS SEEN BY WAVELET DENOISING?

With the noise level threshold we can see good fits by Mittag-Leffler functions to the AR(12) coefficients of the diff(wavelet denoised log(return^2))$ across stocks with which might be considered a natural law of volatility. Of course R^2 is not the best goodness-of-fit measure for nonlinear models but they provide a useful measure of fits that seem visually reasonable at least for economic/financial data which are often dominated by noise. Using the same threshold, the volatility forecasting task produces clearer indication that higher lag models, especially the Mittag-Leffler models quite often outperform the lag-1 model, with some indicative results for 7 stocks.